Related papers: Application of Deep Kernel Models for Certified an…

Data-driven surrogate modeling has emerged as a promising approach for reducing computational expenses of multiscale simulations. Recurrent Neural Network (RNN) is a common choice for modeling of path-dependent behavior. However, previous…

Diffusion kernels over graphs have been widely utilized as effective tools in various applications due to their ability to accurately model the flow of information through nodes and edges. However, there is a notable gap in the literature…

Generating simulated training data needed for constructing sufficiently accurate surrogate models to be used for efficient optimization or parameter identification can incur a huge computational effort in the offline phase. We consider a…

Accurate knowledge of the distribution system topology and parameters is required to achieve good voltage controls, but this is difficult to obtain in practice. This paper develops a model-free approach based on the surrogate model and deep…

The Reduced Basis Method (RBM) is a popular certified model reduction approach for solving parametrized partial differential equations. One critical stage of the \textit{offline} portion of the algorithm is a greedy algorithm, requiring…

Deep learning techniques have been increasingly applied to the natural sciences, e.g., for property prediction and optimization or material discovery. A fundamental ingredient of such approaches is the vast quantity of labelled data needed…

This paper studies the compression of partial differential operators using neural networks. We consider a family of operators, parameterized by a potentially high-dimensional space of coefficients that may vary on a large range of scales.…

Optimal design under uncertainty has gained much attention in the past ten years due to the ever increasing need for manufacturers to build robust systems at the lowest cost. Reliability-based design optimization (RBDO) allows the analyst…

When evaluating quantities of interest that depend on the solutions to differential equations, we inevitably face the trade-off between accuracy and efficiency. Especially for parametrized, time dependent problems in engineering…

Greedy kernel approximation algorithms are successful techniques for sparse and accurate data-based modelling and function approximation. Based on a recent idea of stabilization of such algorithms in the scalar output case, we here consider…

The efficient deployment and fine-tuning of foundation models are pivotal in contemporary artificial intelligence. In this study, we present a groundbreaking paradigm integrating Mobile Edge Computing (MEC) with foundation models,…

Direct numerical simulation of hierarchical materials via homogenization-based concurrent multiscale models poses critical challenges for 3D large scale engineering applications, as the computation of highly nonlinear and path-dependent…

Large language models (LLMs), trained on vast datasets, encode extensive real-world knowledge within their parameters, yet their black-box nature obscures the mechanisms and extent of this encoding. Surrogate modeling, which uses simplified…

Delayed-acceptance is a technique for reducing computational effort for Bayesian models with expensive likelihoods. Using a delayed-acceptance kernel for Markov chain Monte Carlo can reduce the number of expensive likelihoods evaluations…

The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…

The Li-ion battery is a complex physicochemical system that generally takes applied current as input and terminal voltage as output. The mappings from current to voltage can be described by several kinds of models, such as accurate but…

Surrogate models for computational simulations are input-output approximations that allow computationally intensive analyses, such as uncertainty propagation and inference, to be performed efficiently. When a simulation output does not…

Evolutionary illumination is a recent technique that allows producing many diverse, optimal solutions in a map of manually defined features. To support the large amount of objective function evaluations, surrogate model assistance was…

The effective contact area in rough surface contact plays a critical role in multi-physics phenomena such as wear, sealing, and thermal or electrical conduction. Although accurate numerical methods, like the Boundary Element Method (BEM),…

Modeling the evolution of physical systems is critical to many applications in science and engineering. As the evolution of these systems is governed by partial differential equations (PDEs), there are a number of computational simulations…